In the world of machine learning, backpropagation is a central concept that lies at the core of many modern AI applications. This article provides an in-depth look at how backpropagation works and explains why it is so crucial for training neural networks.
What is backpropagation?
Backpropagation, short for „backward propagation of errors“, is an algorithm used in the training phase of neural networks. It is the method by which a neural network learns from its errors. This is done by calculating the error between the actual output of the network and the desired output and then passing it backwards through the network to adjust the weights.
The role of weights in a neural network
To understand the importance of backpropagation, we must first consider the role of weights in a neural network. A neural network is made up of layers of neurons (nodes), and each neuron is connected to many others. Each of these connections has a weight that determines how strongly the signal is transmitted from one neuron to the next.
The training process
- Forward Pass: First, the network outputs a prediction based on the current weights. This phase is called forward pass.
- Calculating the error: Next, we calculate the error, which is the difference between the network’s prediction and the actual desired output. This error is a measure of how „wrong“ the network is.
- Backpropagation: This is where backpropagation comes in. The algorithm works backwards through the network (from the output back to the input) to analyze this error and understand how each weight value contributed to the overall error.
The mathematics behind backpropagation
Backpropagation uses the chain rule of calculus to calculate the partial derivatives of the error with respect to each weight in the network. These derivatives indicate how the error changes when the weights are changed slightly.
Adjusting the weights
After the partial derivatives are calculated, the weights of the network are adjusted. This is usually done using a procedure called gradient descent. The basic idea is to change the weights in the direction that minimizes the overall error. This process is repeated over many iterations, with the network becoming a little more accurate each time.
Source: Kiprono Elijah Koech, How Does Back-Propagation Work in Neural Networks?
After vectorizing the input data, each neuron is assigned a random weight at the beginning. The sum of the weights of all input neurons and the bias of an incoming neuron are sent through an activation function. The goal is to predict the expected value of 1 (in the example image) at the output. In the example, however, 0.521 comes out. This deviation or error is now minimized by backpropagation, i.e., in simple terms, „communicating“ the error to the neurons. In order to do this algorithmically, an error function must be defined. Error functions are Binary Cross Entropy, Mean Square Error, Cosine Distance,
So with this error function our network can see how wrong it is. Of course you could just subtract the predicted value from the expected value, but it turns out that other functions are better suited for calculating this, such as cross entropy.
Since you now have the loss or cost function, you can try to minimize the error using backpropagation and gradient descent, so that the expected value y and the prediction yhat ideally agree.
Why is backpropagation so important?
Backpropagation is crucial to machine learning for several reasons:
- Efficiency: It enables efficient training of deep neural networks consisting of many layers.
- Universality: It can be applied to a wide variety of network architectures, from simple feedforward networks to complex structures such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs).
- Accuracy: By gradually adjusting the weights, backpropagation enables high accuracy in the network’s predictions.
Challenges and limitations
Despite its effectiveness, backpropagation also has challenges and limitations. One of the main problems is the so-called „vanishing gradient“, which occurs when the gradients become too small to effectively train the network. This is especially a problem in deep networks with many layers. In addition, backpropagation can get stuck in local minima, which means that the network finds a suboptimal solution.
ChatGPT, like many modern Large Language Models (LLMs) based on the Transformer architecture, circumvents the vanishing gradient problem through several key techniques and architectural decisions. These methods have made it possible to train more effective and deeper neural networks without falling into the typical vanishing gradient traps.
1. Using the Transformer architecture:
- Skip Connections (Residual Connections): In the transformer models used in ChatGPT, there are so-called „skip connections“ or „residual connections“. These connections pass the input of one layer directly to later layers. This ensures that the signal strength is maintained across many layers and the gradients do not disappear.
- Layer Normalization: Layer Normalization is another important technique in Transformer models. It normalizes the outputs of each layer to ensure that the values remain in a range that is conducive to gradient learning.
2. Attention Mechanism:
- Transformer models, such as the one in ChatGPT, use the attention mechanism, which allows the model to focus on relevant parts of the input. This mechanism is more efficient than the recursive structures used in traditional RNNs (Recurrent Neural Networks) and helps avoid the problem of vanishing gradients.
3. Optimization methods:
- Improved optimizers: ChatGPT uses advanced optimization algorithms such as Adam (Adaptive Moment Estimation) that help make training more stable and reduce the risk of vanishing or exploding gradients.
4. Careful design of the network architecture:
- The architecture of Transformer models is designed to support deep networks without vanishing gradients. This involves carefully tuning the number of layers and the size of the models to find a good trade-off between learning ability and computational requirements.
5. Application of regularization techniques:
- Regularization techniques such as dropout can help prevent the network from learning overly complex patterns, which stabilizes the training process and can mitigate the vanishing gradient problem.
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